Problem Statement

We will call a sequence of length N where each of 1,2,\dots,N occurs once as a permutation of length N.
Given a permutation of length N, P = (p_1, p_2,\dots,p_N), print a permutation of length N, Q = (q_1,\dots,q_N), that satisfies the following condition.

• For every i (1 \leq i \leq N), the p_i-th element of Q is i.

It can be proved that there exists a unique Q that satisfies the condition.

Constraints

• 1 \leq N \leq 2 \times 10^5
• (p_1,p_2,\dots,p_N) is a permutation of length N (defined in Problem Statement).
• All values in input are integers.

Sample Input 1

3
2 3 1

Sample Output 1

3 1 2

The permutation Q=(3,1,2) satisfies the condition, as follows.

• For i = 1, we have p_i = 2, q_2 = 1.
• For i = 2, we have p_i = 3, q_3 = 2.
• For i = 3, we have p_i = 1, q_1 = 3.

Sample Input 2

3
1 2 3

Sample Output 2

1 2 3

If p_i = i for every i (1 \leq i \leq N), we will have P = Q.

Sample Input 3

5
5 3 2 4 1

Sample Output 3

5 3 2 4 1

Problem Statement

You are given an integer sequence A=(A_1,A_2,\dots,A_N) of length N.

Find the maximum value of \displaystyle \sum_{i=1}^{M} i \times B_i for a contiguous subarray B=(B_1,B_2,\dots,B_M) of A of length M.

Notes

A contiguous subarray of a number sequence is a sequence that is obtained by removing 0 or more initial terms and 0 or more final terms from the original number sequence.

For example, (2, 3) and (1, 2, 3) are contiguous subarrays of (1, 2, 3, 4), but (1, 3) and (3,2,1) are not contiguous subarrays of (1, 2, 3, 4).

Constraints

• 1 \le M \le N \le 2 \times 10^5
• - 2 \times 10^5 \le A_i \le 2 \times 10^5
• All values in input are integers.

Sample Input 1

4 2
5 4 -1 8

Sample Output 1

15

When B=(A_3,A_4), we have \displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times (-1) + 2 \times 8 = 15. Since it is impossible to achieve 16 or a larger value, the solution is 15.

Note that you are not allowed to choose, for instance, B=(A_1,A_4).

Sample Input 2

10 4
-3 1 -4 1 -5 9 -2 6 -5 3

Sample Output 2

31

Problem Statement

You are given a string S of length N consisting of digits.

Find the number of square numbers that can be obtained by interpreting a permutation of S as a decimal integer.

More formally, solve the following.

Let s _ i be the number corresponding to the i-th digit (1\leq i\leq N) from the beginning of S.

Find the number of square numbers that can be represented as \displaystyle \sum _ {i=1} ^ N s _ {p _ i}10 ^ {N-i} with a permutation P=(p _ 1,p _ 2,\ldots,p _ N) of (1, \dots, N).

Constraints

• 1\leq N\leq 13
• S is a string of length N consisting of digits.
• N is an integer.

Sample Input 1

4
4320

Sample Output 1

2

For P=(4,2,3,1), we have s _ 4\times10 ^ 3+s _ 2\times10 ^ 2+s _ 3\times10 ^ 1+s _ 1=324=18 ^ 2.
For P=(3,2,4,1), we have s _ 3\times10 ^ 3+s _ 2\times10 ^ 2+s _ 4\times10 ^ 1+s _ 1=2304=48 ^ 2.

No other permutations result in square numbers, so you should print 2.

Sample Input 2

3
010

Sample Output 2

2

For P=(1,3,2) or P=(3,1,2), we have \displaystyle\sum _ {i=1} ^ Ns _ {p _ i}10 ^ {N-i}=1=1 ^ 2.
For P=(2,1,3) or P=(2,3,1), we have \displaystyle\sum _ {i=1} ^ Ns _ {p _ i}10 ^ {N-i}=100=10 ^ 2.

No other permutations result in square numbers, so you should print 2. Note that different permutations are not distinguished if they result in the same number.

Sample Input 3

13
8694027811503

Sample Output 3

840

Problem Statement

There are N - 1 white balls and one black ball. These N balls are arranged in a row, with the black ball initially at the leftmost position.

Takahashi will perform the following operation exactly K times.

• Choose an integer uniformly at random between 1 and N, inclusive, twice. Let a and b the chosen integers. If a \neq b, swap the a-th and b-th balls from the left.

After K operations, let the black ball be at the x-th position from the left. Find the expected value of x, modulo 998244353.

Constraints

• 1 \leq N \leq 998244352
• 1 \leq K \leq 10^5

Sample Input 1

2 1

Sample Output 1

499122178

After one operation, the probabilities that the black ball is at the 1st position and the 2nd position from the left are both \displaystyle \frac{1}{2}. Thus, the expected value is \displaystyle \frac{3}{2}.

Sample Input 2

3 2

Sample Output 2

554580198

Sample Input 3

4 4

Sample Output 3

592707587

Problem Statement

This problem fully contains Problem C (Operate 1), with K \le 20.
You can solve Problem C by submitting a correct solution to this problem for Problem C.

Determine whether it is possible to perform the following operation on string S between 0 and K times, inclusive, to make it identical to string T.

• Choose one of the following three operations and execute it.
  • Insert any one character at any position in S (possibly the beginning or end).
  • Delete one character from S.
  • Choose one character in S and replace it with another character.

Constraints

• Each of S and T is a string of length between 1 and 500000, inclusive, consisting of lowercase English letters.
• K is an integer satisfying \color{red}{1 \le K \le 20}.

Sample Input 1

3
abc
awtf

Sample Output 1

Yes

For example, here is a way to convert abc to awtf with three operations:

• Replace the second character b with w. After the operation, the string becomes awc.
• Replace the third character c with f. After the operation, the string becomes awf.
• Insert t between the second and third characters. After the operation, the string becomes awtf.

Sample Input 2

2
abc
awtf

Sample Output 2

No

abc cannot be converted to awtf with two or fewer operations.

Sample Input 3

17
twothousandtwentyfour
happynewyear

Sample Output 3

Yes